Determining impact of test operations at a product assembly and test facility with repairable products

ABSTRACT

A method and apparatus for establishing an average test time (T A ) include determining a first time interval (T G ) nominally associated with non-failing testing of a unit under test (UUT), and determining a second time interval (T PR ) nominally associated with troubleshooting and repairing a failed unit under test. Additionally, a percent yield (Y) nominally associated with a proportion of non-failing units under test is determined. The average test time is a sum of the first time interval associated with the non-failing testing of the UUT, and a ratio of the second time interval associated with troubleshooting and repair of a failed UUT with respect to the yield.

FIELD OF INVENTION

The present invention relates to conveying information regardingtesting, troubleshooting, and repairing of products at a productassembly facility. More particularly, the present invention relates todetermining how to allocate resources associated with testing productsto improve throughput of such products.

DESCRIPTION OF THE BACKGROUND ART

Manufactures of goods (i.e., products) convert (e.g., assemble) rawmaterials, components, sub-assemblies, and/or the like into finishedproducts. Test operations are implemented either as part or after themanufacturing process to provide quality control and ensure customersatisfaction for the finished products. Test operations are considered areverse-flow process for the product. In particular, if a unit undertest (UUT) fails testing, the failed unit undergoes troubleshooting,repair, and retest. This process continues until the UUT either passesretest or is scrapped.

Product planning is used to estimate when a finished product will beavailable to the consumer. Product planning with respect to testoperations currently includes introducing new product (finished product)at the test facility, where the product is tested and identified aseither passing or failing. Passing product is shipped, while failingproduct is repaired and retested. Specifically, the failed product loopsthrough the repair and test processes until all units have passed.Rarely is an entire system scrapped, since most manufacturing entitiesare high level systems that do not make an allowance for scrap. Morelikely, a sub-system or unit will be replaced. Product planners of testoperations estimate an average test time ({overscore (T)}) required fortesting, troubleshooting, and repairing the finished product.

Specifically, for N units of finished product being tested and a testtime interval of T_(G) to conduct each test, the total test time fortesting N units of finished product is NT_(G). If the percent yield isY, then (1−Y) units must undergo troubleshooting and repair. The timeinterval to troubleshoot and repair a unit under test is T_(PR).Therefore, the total time to test these N units of product is:T=N*T _(G)+(1−Y)*N*(T _(G) +T _(PR)),   (1)where T_(G) represents the time interval to test a product, assuming nofailure during the test, T_(PR) is the time interval to troubleshoot andrepair a failing product, and Y is the yield (proportion of passingunits).

Dividing by N, the Average Test Time estimates are determined by theequation:{overscore (T)}=T _(G)+(1−Y)*(T _(G) +T _(PR))   (2)

Equation (2) represents a first order approximation of the average testtime. The Average Test Time of Equation (2) may be expanded to a secondorder approximation of average test time, in order to account forfailures after the first repair, wherein:T=T _(G)+(1−Y)*(T _(G) +T _(PR))+(1−Y)²*(T _(G) +T _(PR)).   (3)

It is noted that this basic model assumes that the troubleshooting andrepair occurs at the test facility. Therefore, all time incurredconsumes the test facility. When there are no defective products (i.e.,the yield is 100%), the average time per unit is T_(G), which is definedas the good test time in Equation (1).

When the process yields less than perfect product the overall yielddeclines, and the average test time increases significantly from thegood test time interval T_(G). That is, as the yield goes down theaverage time to test a product increases significantly. As will beshown, this first order approximation of Equation (2) for the averagetest time works reasonably well for yields above 80%, while the secondorder approximation of Equation (3) works reasonably well for yieldsabove 70%. However, as the yield drops below 70%, the average test timeestimates provided by Equations (2) and (3) significantly underestimatethe time it will take, on average, to move product through the testprocess.

Thus, current Average Test Time model of Equations (2) and (3) fail toaccount for significant factors that need to be recognized whenestimating the average test time contribution for product planning.Therefore, there is a need in the art for a method and apparatus fordetermining impact of test operations at a product assembly and testfacility with repairable products.

SUMMARY OF THE INVENTION

The disadvantages heretofore associated with the prior art are overcomeby a novel method and apparatus for establishing an average test time(T_(A)). The method and apparatus include determining a first timeinterval (T_(G)) nominally associated with non-failing testing of a unitunder test (UUT), and determining a second time interval (T_(PR))nominally associated with troubleshooting and repairing a failed unitunder test. Additionally, a percent yield (Y) nominally associated witha proportion of non-failing units under test is determined. The averagetest time (T_(A)) is determined according to the relationship ofT_(A)=T_(G)+(T_(G)+T_(PR))((1−Y)Y)).

BRIEF DESCRIPTION OF THE DRAWINGS

The teachings of the present invention can be readily understood byconsidering the following detailed description in conjunction with theaccompanying drawings, in which:

FIG. 1 depicts a high-level block diagram of an exemplary productmanufacturing and assembly facility having a test operations centersuitable for implementing the present invention;

FIG. 2 is a flow diagram of a method for providing test operations atthe manufacturing and assembly facility of FIG. 1;

FIG. 3 depicts a graph representing average test time versus test yield;

FIG. 4 depicts a graph representing average test time versus test yieldin accordance with the principles of the present invention;

FIG. 5 depicts a graph representing shipping performance versus firsttest yield in accordance with the principles of the present invention;

FIG. 6 is a flow diagram of a first subroutine of the method of FIG. 2;

FIG. 7 is a flow diagram of a second subroutine of the method of FIG. 2;

FIG. 8 is a flow diagram of a third subroutine of the method of FIG. 2;

FIG. 9 is a flow diagram of a fourth subroutine of the method of FIG. 2;and

FIG. 10 depicts a graph 1000 illustrating differences between prior artaverage test times versus an average test time in accordance with theprinciples of the present invention.

To facilitate understanding, identical reference numerals have beenused, where possible, to designate identical elements that are common tothe figures.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 depicts a high-level block diagram of an exemplary productmanufacturing and assembly facility 100 having a test operations center102 suitable for implementing the present invention. The exemplaryproduct manufacturing and assembly facility 100 comprises manufacturingand assembly operations 110, test operations 102, a shipping operationscenter 130, and at least one facility controller 120. The manufacturingand assembly operations 110 include labor and machinery 114 thatimplement processes and techniques for systematically convertingspecified resources, such as raw materials, components, subassemblies,and the like, into finished products (goods).

It is noted that the present invention is discussed in terms of massproducing a type of product, such that the term “product” represents aspecific type of good (item), where multiple units of the product areillustratively made sequentially or contemporaneously in lots or inbulk. However, one skilled in the art will appreciate that the presentinvention may be implemented for products made in small quantities orsingle item quantities. Additionally, the products that are manufacturedand/or assembled may form subassemblies for inclusion into otherproducts, such as for example, speakers for inclusion into a multimediadevice (e.g., television or radio). It is further noted that themanufacturing and assembly operations 110 are not considered as part ofthe present invention, however, are included to present a completeunderstanding of the implementation of the present invention withrespect to a product manufacturing and assembly facility 100.

Once the finished products are manufactured and/or assembled, theproducts are tested at the test operations center 102. The testoperations center 102 comprises a testing center 104, a pass testindicator 106, and a troubleshooting center 107 and a repair center 108.The testing center 104 includes test equipment and personnel suitablefor testing and/or inspecting each unit of the product produced by themanufacturing and assembly operations 110. The actual diagnostics andtesting conducted depends on the type of product, its specifications,and requirements associated with quality, reliability, andmaintainability disciplines, as well as the expectations of the end-usercustomer.

In one embodiment, the testing center 104, pass indicator 106, and thetroubleshooting and repair center 108 may be considered as functionalaspects of the test operations center 102, as opposed to separate anddistinct facilities. In this embodiment, a single test and repair deviceor group of test and repair devices may perform two or more of thesefunctional aspects. For example, most test equipment includes some typeof pass and/or fail indicator incorporated into the test equipment.

Once a unit under test (UUT) is tested, a pass (and/or fail) indicator106 provides indicia of whether the tested unit passed or failed thetesting 104. The pass indicator 106 may be any audio device (e.g.,bell), visual device (e.g., colored light), or any other communicationdevice capable of communicating whether the unit passed or failed thetest.

If the UUT passes the testing/inspection during the first time it istested, the unit is sent to the shipping operations center 130 fordelivery to the customer. However, if the tested unit fails, then thefailed unit is sent to the troubleshooting center 107 for diagnostics,followed by the repair center 108 for repair. The troubleshooting center107 and repair center 108 respectively comprise diagnostic and repairequipment, as well as personnel suitable for performing such diagnosticsand repairs for the product. Once the failed unit has been diagnosed andrepaired, the repaired unit is sent back to the testing center 104 forretest. If the repaired unit passes the retest, it is sent to theshipping operations center 130, otherwise it repeats through the repairand retest cycle until it is either properly repaired or scrapped.

The shipping operations center 130 may be any conventional shippingoperation or product transportation department having shipping equipmentand personnel capable of receiving the fully tested final product, andmaking such product available for delivery to the customer. The shippingoperations center 106 does not form a part of the present invention, butis presented for a complete understanding of its relationship to thetest operations center 102 within the context of the manufacturing andassembly facility 100.

The manufacturing and assembly facility 100 further comprises at leastone controller 120 that is suitable for controlling operations at eachof the operation centers and therebetween. Specifically, the controller120 comprises a processor 122, as well as memory 128 for storing variouscontrol programs 129. The processor 122 may be any conventionalprocessor, such as one or more processors illustratively manufactured byIntel Corporation of Santa Clara, Calif. The memory 128 may comprisevolatile memory (e.g., RAM), non-volatile memory (e.g., disk drives)and/or a combination thereof. The processor 122 cooperates with supportcircuitry 124, such as power supplies, clock circuits, cache memory,among other conventional support circuitry, to assist in executingsoftware routines (e.g., method 200) stored in the memory 128.

As such, it is contemplated that some of the process steps discussedherein as software processes may be implemented within hardware, forexample, as circuitry that cooperates with the processor 122 to performvarious steps. It is noted that an operating system (not shown) andoptionally various application programs (not shown) may also be storedin the memory 128 to run specific tasks and enable user interaction. Thecontroller 120 also comprises input/output (I/O) circuitry 126 thatforms an interface between various functional elements communicatingwith the controller 120. It is further noted that the processing stepsof the present invention may be stored in a computer readable medium(i.e., memory devices such as RAM, floppy disk drives, among othermemory devices), which when executed by a processor of, for example, ageneral-purpose computer performs the process steps described herein.

For example, as shown in FIG. 1, the exemplary controller 120 maycommunicate with the devices associated with the manufacturing andassembly operations center 110 via exemplary signal path S_(m), and theshipping operations center 130 via exemplary signal path S_(s).Furthermore, the controller 120 may communicate with the exemplaryfunctional components of the test operations center 102, such as thetesting center 104 via signal path S_(t), the pass test indicator 106via signal S_(p), the troubleshooting center 107 via signal S_(d), andrepair center 108 via signal path S_(r). It is noted that the at leastone controller 120 may also communicate with other functional elements(not shown) of the manufacturing and assembly facility 100, as required.

Although the controller 120 of FIG. 1 is depicted as a general-purposecomputer that is programmed to perform various control functions inaccordance with the present invention, the invention can be implementedin hardware such as, for example, an application specific integratedcircuit (ASIC). As such, it is intended that the processes describedherein be broadly interpreted as being equivalently performed bysoftware, hardware, or a combination thereof. Furthermore, although theexemplary controller 120 is shown as a single controller unit, a personskilled in the art will appreciate that a plurality of controllers maybe implemented at the manufacturing and assembly facility 100 to controlone or more functional aspects of at least one operations center. Insuch embodiment, the plurality of controllers may be organized as anetwork of controllers to provide shared control of the manufacturingand assembly facility 100.

As discussed with respect to FIGS. 2-10, the present invention addressesthe shortcomings of the average test time model set forth in Equations(2) and (3). Specifically, the present invention provides for thepossibility that the first test yield may differ from the retest yield.In one embodiment, the average test time may be computed as:$\begin{matrix}{{\overset{\_}{T} = {T_{G} + {\left( {T_{G} + T_{PR}} \right) \times \left( \frac{1 - Y}{Y} \right)}}},} & (4)\end{matrix}$where T_(G) represents the time interval to test a product, assuming nofailure during the test, T_(PR) is the time interval to troubleshoot andrepair a failing product, and Y is the yield (percentage) of units undertest passing the test the first time.

The average test time under Equation (4) indicates that the testinterval lengthens as the yield decreases. For many product lines, testyields may be low during initial and early product line testingoperations. These low yields may be attributed to undiscovered productdesign flaws, unfamiliarity with testing, troubleshooting, and/or repairof the products, among other early stage product development andmanufacturing. As the learning curves diminish, the failure mechanismshave been identified and resolved, the test operations have been refinedand/or are in a “mature” stage of operation, then the test yields areusually substantially higher. A manufacturer that is producing new typesof products or is in the early stages of test operations needs to havean accurate model of the average test time in order to properly allocateresources (e.g., test equipment, technicians, among other resources), aswell as provide its customers with a realistic schedule for deliveringits finished products.

FIG. 10 depicts a graph 1000 illustrating differences between prior artaverage test times versus an average test time in accordance with theprinciples of the present invention. In particular, the ordinate 1002represents the Average Test Time (e.g., logarithmic scale), and theabscissa 1004 represents the test yield. Curves 1010, 1020, and 1030represent the average troubleshooting and repair time as a multiple ofthe test time. Curve 1010 represents the average troubleshooting andrepair time as computed by the prior art first order approximation ofEquation (2). Curve 1020 represents the average troubleshooting andrepair time as computed by the prior art second order approximation ofEquation (3).

Curve 1030 represents the average troubleshooting and repair time ascomputed by the average test time approximation of the present inventionunder Equation (4). Referring to FIG. 10, for test yields around 70% thethree curves 1010, 1020, and 1030 indicate an average test time between3 to 3.5 time units. However, for test yields below 70%, the timeintervals between the curves diverge. For example, the prior art curves1010 and 1020 respectively associated with the first and second orderapproximations under Equations (2) and (3) have average test times thatare approximately tripled at a ten (10) percent yield, as compared tothe 70% yield for the same. By contrast, the test time approximation ofthe present invention under Equation (4) illustrates that the averagetest time increases approximately one-hundredfold (100×) at the 10% testyield.

As illustratively shown in FIG. 10, the prior art techniques forapproximating average test time are quite inadequate to predict therequired test time required when test yields are below 70%. Suchdeficiencies in prior art test modeling may lead to poor planning interms of allocating resources by the manufacturing entity, as well asfailing to meet customer expectations for delivering the product.

FIG. 3 depicts a graph 300 representing average test time versus testyield. In particular, the ordinate 302 represents the Average Test Time(e.g., logarithmic scale), and the abscissa 304 represents the testyield. Curves 306, through 3065 (collectively curves 306) represent thetroubleshooting and repair time as a multiple of the test time. Sincethe good test time T_(G) is set to one unit of time, the average testtime in the graph represents a multiplier of time and cost for less thanperfect product. For example, curve 3063 represents troubleshooting andrepair time that is three times as long as the good test time T_(G). Thecurves 306 illustrate that as the yield 304 goes down, the average timeto test a product increases significantly. That is, as the test yield304 decreases, the average time to repair increases in a non-linearmanner, such that as the yield approaches zero, the average test timeexceeds 100 units.

Although Equation (4) provides good general purpose model forapproximating average test time over a range of test yields, the AverageTest Time model of Equation (4) does not account for the possibilitythat the yield during repair may differ from the yield during initial(i.e., first) testing of the products. For example, a first test mayyield a 70% pass rate, while the yield after troubleshooting and repairmay be only 60%. If the yield after troubleshooting and repair differs,the actual average test time will be greater than the estimated averagetest time found by using Equation (4). Therefore, unforeseen delays mayoccur while producing product for delivery (i.e., throughput), which maynot be acceptable to a customer for such products.

Another problem is that the average test time defined by Equation (4)does not resolve what may happen if there is a serious process problem,such that the initial yield is zero. By using Equation (4), the averagetest time approaches infinity, which is mathematically correct, butrealistically not very helpful to address customer inquiries regardingwhen they will receive their products.

The present invention modifies Equation (4) such that the average testtime accounts for a first test yield and a retest yield, and is definedas: $\begin{matrix}{{\overset{\_}{T} = {T_{G} + {\left( {T_{G} + T_{PR}} \right) \times \left( \frac{1 - Y_{F}}{Y_{R}} \right)}}},} & (5)\end{matrix}$

-   -   where Y_(F) is the first test yield and Y_(R) is the retest        yield. Equation (5) is distinguished from Equation (4), since        Equation (5) asserts that as long as there is some yield after        going through a troubleshooting and repair loop (e.g., where        Y_(F)=0), eventually all the unit under test (UUT) will be        available for shipment to the customer. It is noted that        Equation (5) is utilized under the assumption that the        troubleshooting and repair processes are being performed on-line        at the test set, as opposed to being performed off-line.

FIG. 4 depicts a graph 400 representing average test time versus testyield in accordance with the principles of the present invention. Thegraph 400 reflects the possibility that the first test time yield Y_(F)and the troubleshooting and repair yield Y_(R) may be different, inaccordance with Equation (5). The graph 400 is the same as graph 300 ofFIG. 3, where curves 406, through 4065 (collectively curves 406)represent the troubleshooting and repair time as a multiple of testtime. However, the curves 406 are drawn by setting the first test yieldY_(F) to zero, and only varying the retest yield YR. Referring to FIG.4, for curve 4063, which represents the 3× repair time curve, at 45%retest yield (and 0% first test yield), the total test time is 10× thegood average test time. If the yield drops, for example, at a 30% retestyield, the total test time is close to 15× the good average test time.Therefore, as the retest yield decreases, the average test timeincreases.

One common technique for enhancing the capacity of a test system is toabort the test upon failure, rather than going through the entire testsequence. In some instances it is not possible to continue a test oncethere is a failure, but in many other situations it could be done. Toaccount for the effect on the average test time due to earlytermination, Equation (5) is modified to the following: $\begin{matrix}{{\overset{\_}{T} = {T_{G} + {\left( {{P_{C}T_{G}} + T_{PR}} \right) \times \left( \frac{1 - Y_{F}}{Y_{R}} \right)}}},} & (6)\end{matrix}$where P_(C) is the percent of the test that is completed prior totermination from the failed test step.

Equation (6) may be used by a planner for the test operations center 102to answer various questions associated with supporting the testing,troubleshooting, and repairing of the products. For example, the totaltime to test, troubleshoot, repair and retest Q units (where Q is apositive number), assuming the assembly time requirements and anyallowance for procuring materials are ignored, is given by:TotalTestTime=Q×T.   (7)

As long as the Total Test Time calculated using Equation (7) is lessthan the allotted time to produce the order (i.e., deliver the order tothe customer), there is no problem. However, if the time required islonger than the allotted time period, then a computation may be made todetermine how many test assets will be required to support the specifiedprogram. If the allotted time period is T_(PD), and the time a testasset is available within that interval is T_(SA), (whereT_(SA)<T_(PD)), then the number of test systems required is:$\begin{matrix}{{\#{TestSystemsNeeded}} = {\frac{Q \times \overset{\_}{T}}{T_{SA}}.}} & (8)\end{matrix}$

A person skilled in the art will appreciate that it is not possible tohave a fraction of a test system. Therefore, for a test system that isdedicated to only one product, the principle options available includerounding up to the next integer number of test systems, working extendedhours on the current staffing plan, and/or adding shifts to provide moreavailability. The rounding up of test systems option may be acceptableunder two conditions: (i) if the fraction is a large portion of a testsystem (e.g., >50%), and (ii) if the cost of the system is smallcompared to the costs incurred utilizing other alternatives.

The option of working extended hours on existing shifts may be anacceptable and economical choice, although it is best applied when thelength of time for additional capacity is short. Working longer hours ona routine basis has been observed to diminish the workers effectiveness.The option of adding a shift may be prudent when (i) the work load willbe for an extended period of time, and (ii) the facilities cost is high.

There are other possible options, depending on the lead-time availableto implement a plan. For example, depending on the amount of lead-time,a planner might consider trying to improve the yield or shorten the testtime to effectively generate additional capacity. In addition,off-loading some of the work from the test system, e.g. repair ortroubleshooting may also be an option, as discussed below in furtherdetail.

Another question that may be answered by Equation (6) is how manyassociates are required to support the execution of the specifiedprogram. In a manor similar to the number of test systems required, thestaffing level is given by: $\begin{matrix}{{{{Staff}\quad\#} = \frac{Q \times \overset{\_}{T}}{T_{AA}}},} & (9)\end{matrix}$

where T_(AA) is the time each staff member is available within theallotted time period T_(PD). It is noted that the discussion associatedwith Equation (8) is applicable with respect to Equation (9) as well.

Given the loaded rate per time period of the operator performing thetest, C_($T), the average cost is given by:Cost/unit=C _($T) ×{overscore (T)}.   (10)Based on Equation (6), the average cost for troubleshoot, repair andretest is:Cost/unit=C _($T)×({overscore (T)}−T _(G))   ( 11)

The troubleshooting, repair, and retest (TS&R) costs are a part of theaverage cost to test a unit. This TS&R cost may be a significant part ofthe total cost if the first test yield Y_(F) is low or if the ability todiagnose failures is poor (this leads to low Y_(R)), or if the time toperform troubleshooting or repair is excessive (large T_(PR)).

Equation (6) may also be utilized to help determine a particular actionto take, for example, if additional resources are available to improvethe process. Such additional resources may illustratively be used toreduce the test time T_(T), reduce the troubleshoot/repair time T_(PR),or improve the yields Y_(F) and Y_(R). Although there is no one correctanswer (other than “it depends”), Equation (6) can be differentiatedwith respect to each of the independent variables.

Thus, a change in average test time T_(A) caused by a change in the goodtest time T_(G) is given by: $\begin{matrix}{{\Delta\quad\overset{\_}{T}} = {\left( {1 + {P_{C}\left( \frac{1 - Y_{F}}{Y_{R}} \right)}} \right) \times \Delta\quad{T_{G}.}}} & (12)\end{matrix}$

Moreover, a change in the average test time T_(A) caused by a change inthe troubleshoot and repair (retest) time T_(PR) is given by:$\begin{matrix}{{\Delta\quad\overset{\_}{T}} = {\left( \frac{1 - Y_{F}}{Y_{R}} \right) \times \Delta\quad{T_{PR}.}}} & (13)\end{matrix}$

A change in average test time T_(A) caused by a change in yield Y isgiven by the two equations: $\begin{matrix}{{{\Delta\quad\overset{\_}{T}} = {{- \frac{\left( {{P_{C}T_{G}} + T_{PR}} \right)}{Y_{R}}} \times \Delta\quad Y_{F}}},} & (14)\end{matrix}$

which represents the impact of a change in First Test Yield, and$\begin{matrix}{{{\Delta\quad\overset{\_}{T}} = {{- \left( {{P_{C}T_{G}} + T_{PR}} \right)}\left( {1 - Y_{F}} \right) \times \frac{Y_{R\quad 2} - Y_{R\quad 1}}{Y_{R\quad 2} \times Y_{R\quad 1}}}},} & (15)\end{matrix}$

which represents the impact of a change in Repair test yield.

It is a responsibility of test operations managers to use the resourcesavailable to them efficiently, since the test systems represent the mostsignificant investment in the final assembly and test (FA&T) operations.Thus, it is important to be able to determine how effectively thecapital resources are being used. From the previous analysis of Equation(8), the number of test systems required may be determined, and caveatswere given on why it might be prudent to install more facilities thanthe calculation indicated. If the actual number of test systems deployedis N_(S), then the percent utilization of the test systems may bedetermined.

The percent utilization represents the fraction of available time thefacility is in use. This is a measure of how well resources are beingemployed, such as the test systems, which may be expensive. Utilizationmay range from 0% (you are not using the facility at all) to 100% (fullusage). However, as a practical matter, typical utilization is maximizedat approximately 85%, since levels above 85% usually are beyondmanagement's ability to efficiently manage the people who staff thefacility, maintenance, and the like. The percent utilization is givenby: $\begin{matrix}{{Utilization} = {\frac{Q \times \overset{\_}{T}}{N_{S} \times T_{SA}} \times 100{\%.}}} & (16)\end{matrix}$

The embodiment of the average test time T_(A) as per Equation (6), andthe subsequent corresponding Equations (7-16) of the present inventionmay best be understood by the following example. An order,illustratively, for 200 pieces of a particular product is received bythe manufacturing and assembly facility 100, with customer deliveryrequested in two weeks. For this example, the product historically has agood test time of one hour, a troubleshooting and repair time of threehours (3×), a first test yield Y_(F) of 70%, and a retest yield Y_(R) of60%. The operation is run five days, two shifts, and each associateworks forty hours per week. The portion of the test completed P_(C) whena failure occurs is 50% on average.

Starting with the average test time per product which is given byEquation (6), the Average Test Time is:$\overset{\_}{T} = {{T_{G} + {\left( {{P_{C}T_{G}} + T_{PR}} \right) \times \left( \frac{1 - Y_{F}}{Y_{R}} \right)}} = {\overset{\_}{T} = {{1 + {\left( {{{.5} \times 1} + 3} \right) \times \frac{1 - {70\%}}{60\%}}} = {2.75\quad{{hours}.}}}}}$The number of test systems required to support a projected productionprogram may be found from Equation (7), where TotalTestTime=Q×{overscore(T)}=200×2.75 hours=550 Hrs.

With the operation running a five (5) days, each day having two (2)shifts, there are 80 hours per week available, so for two weeks thereare 160 hours of test system capacity. Thus, from Equation (8) thenumber of test systems required is:${\#{TestSystemsNeeded}} = {\frac{Q \times \overset{\_}{T}}{T_{S\quad A}} = {\frac{550}{160} = {3.44.}}}$system, a decision needs to be made regarding how to handle thecustomers' need. One possible solution is to round up to four testsystems; In this instance, there will be more than enough capacity, andnothing else needs to change. However, this first solution will requiretying up additional capital that may impact the utilization of thefacility resources.

A second solution is to ask the customer to spread out the acceptance ofthe product over a longer time interval. In some instances this may beacceptable, although a drawback may be a loss of confidence by thecustomer to meet production schedules.

A third solution is to work additional hours within the time periodrequested by the customer. This solution may be satisfactory, as long asthe necessary human resources are available to perform the work.However, prolonged use of overtime tends to overburden the staff, andconsequently lower their productivity. These three solutions arediscussed below in further detail with respect to assessing utilization.

The cost added to each product for the testing is derived from Equation(10). Assuming $100 per hour for a fully loaded testing rate, Cost[Unitis: Cost/unit=C_($T)×{overscore (T)}=$100×2.75=$275.00.

The cost added to each product for troubleshooting/repair and retest isderived from Equation (11), where Cost/unit=C_($T)×({overscore(T)}−T,)=$100×(2.75−1)=$175.00. It is noted that the cost added into theaverage, is more than the cost of a good test ($100), while 70% of theproducts pass the first time. Further, the average expenditure for eachfailing unit is $583 in addition to the good test cost,${{where}\frac{{Avg}\quad{repair}\quad{cost} \times {volume}}{\left( {1 - Y} \right)*{volume}}} = {\frac{{\$ 175} \times 100}{\left( {1 - {70\%}} \right) \times 100} = {\frac{\$ 17500}{30} = {{\$ 583}{{.33}.}}}}$

In other words, the 30 units that require repair each cost $583 torepair and drive the average cost up by $175. This is the motivatingforce behind most quality movements, such as TQM, Six Sigma, among otherquality related organizations and movements.

If additional resources are available to improve the process, adetermination of how such additional resources should be utilized ismade. In particular, the additional resources may be used to reduce thetest time, reduce the troubleshoot/repair time, or improve the yield.

Assume that for a $3000 investment, a 10% improvement in good test time,or a 10% improvement in troubleshoot and repair time, or a 10%improvement in either the first test yield Y_(F) and/or the repair yieldY_(R) may be achieved. Equations (12-16) may be utilized to determinehow the $3000 should be invested. Specifically, from Equation (12) thesavings for a change in good test time T_(G) is computed as${\Delta\quad\overset{\_}{T}} = {{\left( {1 + {P_{C}\left( \frac{1 - Y_{F}}{Y_{R}} \right)}} \right) \times \Delta\quad T_{G}} = {{\left( {1 + {0.5\left( \frac{1 - {.70}}{.6} \right)}} \right) \times \left( {1\quad{Hr} \times 10\%} \right)} = {0.20\quad{{hr}.}}}}$

From Equation (13), the savings for a change in the troubleshoot andrepair time${T_{R}\quad{is}\quad\Delta\quad\overset{\_}{T}} = {{\left( \frac{1 - Y_{F}}{Y_{R}} \right) \times \Delta\quad T_{PR}} = {{\left( \frac{1 - {70\%}}{75\%} \right) \times \left( {3 \times 10\%} \right)} = {0.15\quad{{hr}.}}}}$

From Equation (14) the savings for a change in the first test yieldY_(F) is:${\Delta\quad\overset{\_}{T}} = {{{- \frac{\left( {{P_{C}T_{G}} + T_{PR}} \right)}{Y_{R}}} \times \Delta\quad Y_{F}} = {{{- \frac{\left( {{0.5 \times 1} + 3} \right)}{0.6}} \times (0.07)} = {0.408\quad{{hr}.}}}}$

From Equation (15) the savings for a change in repair test yield Y_(R)is:${\Delta\quad\overset{\_}{T}} = {{{- \left( {{P_{C}T_{G}} + T_{PR}} \right)}\left( {1 - Y_{F}} \right) \times \frac{Y_{R\quad 2} - Y_{R\quad 1}}{Y_{R\quad 2} \times Y_{R\quad 1}}} = {{{- \left( {{0.5 \times 1} + 3} \right)}\left( {1 - 0.7} \right)\left( \frac{0.66 - 0.6}{0.6} \right)} = {0.105\quad{{hr}.}}}}$

Thus, Equations (12-14) show that for this example, the greatest savingscomes from improving the first test yield Y_(F), since the most hours(0.408 hrs) will be saved. Furthermore, by investing the capital toimprove the first test yield Y_(F), the cost of the improvement on theorder for 200 pieces will produce a savings ofSavings=200×0.408×$100=$8160. Since it will cost $3000 to implement theimprovement, the net savings will be $5160 ($8160−$3000).

The number of associates (staff personnel) required to support theexecution of the planned program is derived from Equation (9). From theexemplary information provided above, the staffing level needed is:${{Staff}\quad\#} = {\frac{Q \times \overset{\_}{T}}{T_{AA}} = {\frac{550}{40 \times 2} = {6.875.}}}$Since a fractional number is determined, a decision to round up or workovertime must be analyzed in view of the external factors discussedabove.

Finally, Equation (16) may be used to determine how effectively thecapital resources are being utilized. Two different options are used forthis utilization calculation. A first option is to round up the numberof test systems to four test systems. From Equation (16), theutilization when four test systems are implemented is:${Utilization} = {{\frac{Q \times \overset{\_}{T}}{N_{S} \times T_{SA}} \times 100\%} = {{\frac{550}{4 \times 160} \times 100\%} = {85.9\%}}}$

For the second option, three test systems are used, but eight hours ofovertime are worked on Saturday for each shift. From Equation (16)working overtime, the available hours are changed to match what is beingused.${Utilization} = {{\frac{Q \times \overset{\_}{T}}{N_{S} \times T_{SA}} \times 100\%} = {{\frac{550}{3 \times 192} \times 100\%} = {95.5{\%.}}}}$Although the second option appears to produce almost 10% greaterutilization, consideration needs to be given to the possibility ofsystem outage or down time, uneven flow of material, availability ofoperators, among other problems that may occur at the manufacturing andassembly facility 100. It is noted that there is no right answer, butrather a carefully assessed review of the risks being taken is provided.

The Average Test Time of Equation (6) may also be used to determine howdoes the test yield impact profitability. From the example used above,it is assumed that the conditions set there were the planned operatingpoint. Specifically, plans were made using these values as the expectedperformance level, and expectations were set based on them (i.e.,commitments to customers for shipping dates). The conditions include thegood test time T_(G) is 1 hour; the troubleshooting and repair timeT_(R) is 3× the good test time (i.e., 3 hours); the cost for test, aswell as assembly C_($T) is $100 per hour; it takes one hour to assemblethe product; and the average test time for 70% yield is 2.75 hours perEquation (6).

At $100 per hour the labor cost for one-hour assembly and 2.75 hours oftest is $375 ($100+$275). Assuming the $375 combined assembly and testcost represents five percent (5%) of the total manufacturing cost, thenthe total manufacturing cost is $7500. If the product is listed to sellat a price at two and one-half times the manufacturing cost,consequently the product sells for $18,750. It is assumed that thecompany is planning to earn a 35% gross margin (i.e., the differencebetween the selling price and the total costs). In this case the grossmargin is $6562.50 ($18750×0.35).

With the above assumptions and conditions, a determination may be madefor what happens if a problem occurs that illustratively drops the firsttest yield (e.g., 50%). First, by putting 50% into the average test timeEquation (6), the average test time is increases to 3.92 hours from theprevious 2.75 hours. This represents an additional 1.17 hours of time,and $117 in cost in excess of the plan. If the gross margin is reducedby $117, to $6445.50, the margin becomes 34.38%, a reduction of 0.62%,which is a significant and undesirable result.

The Average Test Time of Equation (6) may also be used to determine howa change in yield affects delivery performance. As a manufacturerstrives to meet or exceed its customer's expectations, it is veryimportant that the manufacturer keep the promises made to its customers.These promises include delivery performance, which may be monitored byvarious delivery performance metrics. Here delivery performance isdefined as a percentage or ratio of the number of products shipped ontime, divided by the total number of products promised during thespecified interval.

The discussion above examined how yield influences the time it takes toget the product through the test process. However, for purposes offurther understanding the invention, the above example is expanded tolook at the effect a change in yield has on the manufacturer's abilityto ship the product when promised. It is assumed that the assemblyinterval is steadfast, and that the test operation 102 is theconstraining resource.

It is desirable to know how to establish an interval for the testprocess that allows the manufacturer to meet the delivery performancemetric. One way to make this determination is by looking at the testoperations 102. In particular, since the test operation 102 is being runin such a manner that if a buffer preceding the test operations 102always has assembled product stored therein, the only constraint on theability to ship is how quickly product can be moved through the testprocess.

For a customer order of 100 units of the product, and the average testtime being 2.75 hours, the manufacture can process (i.e., test)1/2.75=0.364 units per hour. To process 100 units, it will take100/0.364=275 hours. If during normal operations there is an expecteddowntime on the test system for maintenance and/or other unplannedevents, a margin of safety must be built in to the process. In thisexample, the margin of safety is set to 15%, such that production isscheduled to utilize 85% of the systems capacity. This means the plannedtime testing will consume is 275/0.85=323.5 hours during the testing ofthis product. Thus, the manufacturer may commit to its customer that itcan ship the 100 unit order in 323.5 hours.

FIG. 5 depicts a graph 500 representing shipping performance versusfirst test yield in accordance with the principles of the presentinvention. The graph 500 of FIG. 5 may be used to see what happens whenthe first test yield changes. The graph 500 comprises and ordinate 502representing how many units of the product ship, and an abscissa 504representing the first test yield. The curve 506 represents the shippingperformance versus the first test yield Y_(F) in accordance withEquation (6). Referring to curve 506, it is noted that the manufactureris illustratively able to ship the entire order on time if the firsttest yield Y_(F) drops from 70% to 62% for this example. Moreover, themanufacturer can still ship 95% of the order if the first test yieldY_(F) drops down to 59%. These numbers reflect the fact that themanufacture has included a 15% margin of safety in order to account fordowntime occurrences of the test operations 102.

In a second embodiment of the invention, the average test time isdetermined by distinguishing between the actual time it takes to performthe troubleshooting (T_(p)), and the actual time it takes to perform therepairs (T_(R)). Further, time is accounted for loading each unit undertest, as well as disconnecting each unit under test from the testequipment.

FIG. 2 is a flow diagram of a method 200 for providing test operationsat the manufacturing and assembly facility of FIG. 1. The flow diagramof FIG. 2 is formed by a plurality of sub-routines 602, 702, 802, and902 that collectively define the test operations 102 under variousoperating conditions. FIGS. 6-9 depict flow diagrams of each of thesesubroutines, and should be viewed along with FIGS. 1 and 2.

In particular, the subroutine 602 illustrates testing each product usingonline troubleshooting and online repair prior to the product beingshipped. Subroutine 702 illustrates testing each product using onlinetroubleshooting and off-line repairs being made to defective productprior to the product being shipped. Subroutine 802 illustrates testingeach product using off-line troubleshooting and online repairs prior tothe product being shipped. Alternatively, subroutine 902 illustratestesting using both offline troubleshooting and offline testing prior tothe product being shipped. The steps in each routine are respectivelydescribed in detail with respect to FIGS. 6-9.

FIG. 6 is a flow diagram 600 of a first subroutine 602 according to themethod 200 of FIG. 2. Recall that Equation (6) provides that the averagetest time$\overset{\_}{T} = {T_{G} + {\left( {{P_{C}T_{G}} + T_{PR}} \right) \times {\left( \frac{1 - Y_{F}}{Y_{R}} \right).}}}$Referring to FIG. 6, the subroutine 602 divides the test time T_(G) intothe various components. At 610, T_(C) is the time interval to set up thetest system and get it prepared to perform the product testing. Suchpreparation may include power up the test system, connecting anyassociated fixtures, loading applicable programs, and the like. The testsystem preparation does not need to be done separately for each unittested, but may be performed, illustratively, for each lot of producttested. At 612, T_(L) represents the time to connect (load) the product(unit under test (UUT) to the test system. For some products this timemay be significant, depending on the complexity of the product (e.g.,numerous I/O ports, multifunctional properties of the products, amongother test related requirements). At 614, T_(T) represents the time ittakes to test a good unit once it is connected to the test system.

At 616, a determination is made whether the UUT passes the testing.Specifically, a determination is made whether the product passed thetest. For an individual product, this is a binary decision, i.e., yes orno. For the more general case, it is the product yield, i.e., theproportion of units that passed test. The subroutine 602 proceeds to618, where the good UUT is disconnected. Disconnecting the UUT from thetest equipment consumes a first disconnect time T_(D1), and like theload time T_(L), is also dependent on the complexity of the product.

At 620, the UUT is prepared for shipping, logging out, and shipped,which consumes a shipping time T_(S). The additional disconnecting andshipping times T_(D) and T_(S) after the unit passes test, allows foridentifying operations that may consume test system capacity that maynormally be missed by the prior art techniques. Depending on thesituation, the disconnecting and shipping operations may both beperformed by the test system operator or they may be split. For example,the test system operator may perform the disconnecting operation of theUUT, while another operator performs the post-test shippingpreparations. If there are no units scrapped then each unit will incurthese two times.

If at 616, the UUT does not pass product testing, the defective UUTundergoes the troubleshooting and repair operation as discussed above.In particular, the troubleshooting and repair time T_(PR) has beenbroken into two significant concerns. At 624, T_(P) represents the timeinterval required to perform troubleshooting (diagnostics), while 628represents the time interval required to perform the repair T_(R). Forthe subroutine 600 of FIG. 6, T_(P1) represents the time intervalrequired to perform on-line troubleshooting (diagnostics), while 628represents the time interval required to perform on-line repairs T_(R1)of the failed unit.

Looking at the average test time, the relationships described above maybe substituted into Equation (6) by making an assumption that theaverage lot size equals n. Thus, the Average Test Time is modified to:$\begin{matrix}{\overset{\_}{T} = {\left( \frac{T_{C}}{n} \right) + T_{L} + T_{T} + {\left( {{P_{C}T_{T}} + T_{P\quad 1} + T_{R\quad 1}} \right) \times \left( \frac{1 - Y_{F}}{Y_{R}} \right)} + T_{D\quad 1} + {T_{S}.}}} & (17)\end{matrix}$

One skilled in the art will appreciate that Equations (7-16) may also bemodified in view of Equation (17). For example, the averagetroubleshooting/repair and retest cost C_($T) added to each productunder subroutine 602 is:${{Cost}/{unit}} = {C_{\$\quad T} \times {\left( {{\overset{\_}{T}}_{A} - \left( {\frac{T_{C}}{n} + T_{L} + T_{T} + T_{D\quad 1} + T_{S}} \right)} \right).}}$A change in the good test time is given by:${\Delta\quad{\overset{\_}{T}}_{A}} = {\left( {1 - {P_{C}\left( \frac{1 - Y_{F}}{Y_{R}} \right)}} \right) \times \Delta\quad{T_{T}.}}$A change in the troubleshoot time is given by:${\Delta\quad{\overset{\_}{T}}_{A}} = {\left( \frac{1 - Y_{F}}{Y_{R}} \right) \times \Delta\quad{T_{P\quad 1}.}}$A change in the repair time is given by:${\Delta\quad{\overset{\_}{T}}_{A}} = {\left( \frac{1 - Y_{F}}{Y_{R}} \right) \times \Delta\quad{T_{R\quad 1}.}}$A change in yield is given by:${{\Delta\quad{\overset{\_}{T}}_{A}} = {{- \frac{\left( {{P_{C}T_{T}} + T_{P\quad 1} + T_{R\quad 1}} \right)}{Y_{R}}} \times \Delta\quad Y_{F}}},{{{and}\quad\Delta{\overset{\_}{T}}_{A}} = {{- \left( {{P_{C}T_{T}} + T_{P\quad 1} + T_{R\quad 1}} \right)}\left( {1 - Y_{F}} \right) \times {\frac{Y_{R\quad 2} - Y_{R\quad 1}}{Y_{R\quad 2} \times Y_{R\quad 1}}.}}}$

Recalling the basic assumption that the test system is the bottleneckfor throughput of a finished product and that the goal is to maximizeits utilization, the revised model under Equation (17) may be separatedinto activities that must be performed on the test system, to thoseactivities that may or may not be performed at the test system. The timevalues T_(C), T_(L), T_(T), and T_(D) are all related to the test systemand must be done at the test system. However, the times associated withother operations, such as troubleshooting T_(P1) repair T_(R), andshipping T_(S), have various options, depending on the product andtechnology.

One option to consider is whether to perform the troubleshooting offailed units on the test system. Troubleshooting may consume largeamounts of time and significantly reduce capacity if performed on thetest system. On the other hand, a separate test facility may be used toperform the troubleshooting, and in most cases it will be substantiallyless expensive than the system test set. If not, the economics must bereviewed very carefully.

A second option is whether to perform the repair of the product at thepoint where the diagnosis (troubleshooting) of the problems occur.Repairs may be performed at the test system or at a troubleshootingfacility. Performing the repair at the test system location consumescapacity of higher priced assets. In addition, there may be technical orpractical reasons for performing the repair at a separate location(e.g., troubleshooting facility).

FIG. 6 represents the subroutine 602 of FIG. 2 where the troubleshootingis performed on-line and the repair is also performed on-line at thetest set. Specifically, at 616, if the UUT does not pass testing, thesubroutine 602 proceeds to 622. At 622, a determination is made whetherto troubleshoot on-line. That is, a determination is made whether thefailing UUT is troubleshot at the current test system (on-line). For anindividual unit, the decision is binary, i.e., yes or no. For the moregeneral case, this may be a proportion of the units that are troubleshotat the test system. If the determination is negatively answered, thesubroutine 602 proceeds to subroutine 802, as discussed below in furtherdetail.

If at 622, the determination is affirmatively answered, then thesubroutine 602 proceeds to 624, where the failed UUT undergoesdiagnostics to identify the failure. Once troubleshooting is complete,at 626, a determination is made whether to repair at the test set. Ifthe determination is negatively answered, the subroutine 602 proceeds tosubroutine 702, as discussed below in further detail.

If at 626, the determination is affirmatively answered, then thesubroutine 602 proceeds to 628, where the failed UUT is repaired. Thatis, a determination is made whether the repair work will be performed atthe test system. For an individual unit this is a binary decision, i.e.,yes or no. In general this can represent the proportion of units thatare repaired at the test system. Once the repair is complete, thesubroutine returns to 614 where the repaired UUT is retested, andsubroutine 602 is repeated until the UUT passes testing at 616.

FIG. 7 is a flow diagram 700 of a second subroutine 702 according tomethod 200 of FIG. 2. The flow diagram 700 includes steps 610-626 ofsubroutine 602, except at 626, a determination is made that the repairis not being performed at the current test set (i.e., repairs are madeoff-line). That is, subroutine 702 provides for on-line troubleshootingat the current test set, but off-line repairs. This means at 626, if thedetermination whether to make the repair at the test set is negativelyanswered, the subroutine proceeds to 710, where the failed UUT isdisconnected. The time associated with disconnecting the UUT from thetest on-line troubleshooting equipment is T_(D1), as discussed abovewith step 618 of subroutine 602. At 712, the failed UUT is shipped to arepair facility. The time T_(M2) associated with moving (e.g., shipping)the failed UUT to a workstation at a repair facility depends on numeroustransportation and handling requirements, such as size, packagingrequirements, test set location, among other shipping and handlingrequirements. It is noted that the off-line test set may be locatedwithin the same repair facility as where troubleshooting occurs or atanother location. The only qualification is that the offline repairs arenot performed on a test set that was used to run the first test of thefinal product.

At 714, the failed UUT is repaired, and at 716, the repaired UUT isshipped back to the test set. The time associated with repairing the UUTat a workstation is T_(R3), while the time for moving (e.g., shipping)the repaired UUT from the workstation back to the test set is T_(M4). Asnoted above, the repair time is dependent on the type of product andskill level of the persons making such repairs. The shipping time backto the test set is dependent on various shipping and handling factors(location, size, packaging requirement, among other factors), asdiscussed above. Once the repaired UUT is shipped back to the test set,subroutine 602 is performed such that at 612, the repaired UUT is loadedonto the test set, at 614, the repaired UUT is retested, and if itpasses retest, is shipped at 620. Otherwise, if the UUT fails retest,subroutine 702 is repeated, as discussed above.

Adapting Equation (17) for subroutine 702, the average test time may beexpressed as: $\begin{matrix}{{\overset{\_}{T}}_{A} = {\frac{T_{C}}{n} + T_{L} + T_{T} + {\left( {{P_{C}T_{T}} + T_{P\quad 1} + T_{D\quad 1} + T_{L}} \right) \times \left( \frac{1 - Y_{F}}{Y_{R}} \right)} + {T_{D\quad 1}.}}} & (18)\end{matrix}$

The average product test time is: $\begin{matrix}{{\overset{\_}{T}}_{B} = {\frac{T_{C}}{n} + T_{L} + T_{T} + {\left( {{P_{C}T_{T}} + T_{P\quad 1} + T_{D\quad 1} + T_{M\quad 2} + T_{R\quad 3} + T_{M\quad 4} + T_{L}} \right) \times \left( \frac{1 - Y_{F}}{Y_{R}} \right)} + T_{D\quad 1} + {T_{S}.}}} & (19)\end{matrix}$

The average troubleshooting/repair and retest cost added to each productis,${{Cost}/{unit}} = {C_{\$\quad T} \times {\left( {{\overset{\_}{T}}_{B}\left( {\frac{T_{C}}{n} + T_{L} + T_{T} + T_{D\quad 1} + T_{S}} \right)} \right).}}$The troubleshooting, repair, and retest (TS&R) cost is a part of theaverage cost to test a unit. This TS&R cost can be a significant part ofthe total cost if the yield is low or if the ability to diagnose andrepair failures is poor (large T_(P1), or T_(R3)).

A change in average test time caused by a change in the good test timeis given by:${\Delta\quad{\overset{\_}{T}}_{A}} = {{\Delta\quad{\overset{\_}{T}}_{B}} = {\left( {1 - {P_{C}\left( \frac{1 - Y_{F}}{Y_{R}} \right)}} \right) \times \Delta\quad{T_{T}.}}}$A change in average test time caused by a change in the troubleshoottime is given by:${\Delta\quad{\overset{\_}{T}}_{A}} = {{\Delta\quad{\overset{\_}{T}}_{B}} = {\left( \frac{1 - Y_{F}}{Y_{R}} \right) \times \Delta\quad{T_{P\quad 1}.}}}$A change in average test time caused by a change in the repair time isgiven by:${{\Delta\quad{\overset{\_}{T}}_{A}} = 0},{{\Delta\quad{\overset{\_}{T}}_{B}} = {\left( \frac{1 - Y_{F}}{Y_{R}} \right) \times \Delta\quad{T_{R\quad 3}.}}}$

A change in average test time caused by a change in yield is given by:${{\Delta\quad{\overset{\_}{T}}_{A}} = {{- \frac{\left( {{P_{C}T_{T}} + T_{P\quad 1} + T_{D\quad 1} + T_{L}} \right)}{Y_{R}}} \times {\Delta Y}_{F}}};{{\Delta\quad{\overset{\_}{T}}_{B}} = {{- \frac{\left( {{P_{C}T_{T}} + T_{P\quad 1} + T_{D\quad 1} + T_{M\quad 2} + T_{R\quad 3} + T_{M\quad 4} + T_{L}} \right)}{Y_{R}}} \times \Delta\quad Y_{F}}};$${{\Delta\quad\overset{\_}{T}} = {{- \left( {T_{T} + T_{P\quad 1} + T_{D\quad 1} + T_{M\quad 2} + T_{R\quad 3} + T_{M\quad 4} + T_{L}} \right)} \times \frac{Y_{R\quad 2} - Y_{R\quad 1}}{Y_{R\quad 2} \times Y_{R\quad 1}}}};{and}$${\Delta\quad\overset{\_}{T}} = {{- \left( {T_{T} + T_{P\quad 1} + T_{D\quad 1} + T_{M\quad 2} + T_{R\quad 3} + T_{M\quad 4} + T_{L}} \right)} \times {\frac{Y_{R\quad 2} - Y_{R\quad 1}}{Y_{R\quad 2} \times Y_{R\quad 1}}.}}$

FIG. 8 is a flow diagram 800 of a third subroutine 802 according tomethod 200 of FIG. 2. Subroutine 802 provides for off-linetroubleshooting and on-line repairs. The flow diagram 800 includes steps610-622 of subroutine 602, except at 622, a determination has been madethat troubleshooting is to be performed off-line (i.e., not at thecurrent test set). The subroutine then proceeds to 810 of subroutine802. At 810, the failed UUT is disconnected in a time of T_(D1), whichas discussed above, depends on the complexity of the product and testequipment. The subroutine 802 then proceeds to 812.

At 812, the failed UUT is transported (e.g., packed and shipped) to atroubleshooting facility. The troubleshooting facility may be located atthe manufacturing and assembly facility 100 or other locations (e.g., avendor). The time associated with moving (e.g., shipping) T_(M1) thefailed UUT is product dependent, as discussed above with respect to thetransportation time T_(M2) when transporting a UUT to a workstation at arepair facility at 712 of subroutine 702. It is noted that the UUTmoving times T_(M1) through T_(M4) are denoted as having differenttransportation (e.g., packed and shipping) times, since the locations ofthe on-line troubleshooting facilities, and on-line/off-line repair testsets may all be different.

At 814, the failed UUT undergoes troubleshooting. The time T_(P2)associated with off-line troubleshooting may differ from the time T_(P1)for on-line troubleshooting. The troubleshooting time differences may beattributed to, but are not limited to, different types of diagnosticsequipment utilized at each location, skill level of the technicians,ability to perform specialized measurements ( the system test set maynot be as flexible in this regard compared to a troubleshootingstation), and the like. Once troubleshooting is complete at 814,subroutine 802 proceeds to 816.

At 816, a determination is made whether repairs are to be performed atthe test system position. That is, a determination is made whether therepair work will be performed at the off-line troubleshooting station.For an individual unit this is a binary decision, i.e., yes or no. Ingeneral this is the proportion of units that get repaired at thetroubleshooting station.

If the determination at 816 is negatively answered, the subroutine 802proceeds to subroutine 902, as discussed below in further detail.Otherwise, if the determination is affirmatively answered, thesubroutine 802 proceeds to 818, where an on-line (i.e., at the same testset) repair is made. The time associated with the on-line repair isT_(R2), as compared to the on-line repair is T_(R3) associated withoff-line repairs at a workstation, as discussed with respect to 714 ofsubroutine 702. The repair time differences may be attributed to, butare not limited to, specialized repair location may have tools to removeand reapply components more efficiently than those at a test ortroubleshooting station. In some instances certain components requirespecialized tools or facilities to remove and reattach them. Once repairaction is complete at 818, subroutine 802 proceeds to 820.

At 820, the repaired UUT is disconnected a from the repair equipment. Itis noted that the time associated with disconnecting the UUT from theon-line repair is T_(D2). The disconnect time T_(D2) may differ from thedisconnect time T_(D1) associated with disconnecting the UUT from theoff-line diagnostics equipment, as discussed with respect to 810. Thedisconnect time differences may be attributed to, but are not limited todifferences in types of repair equipment used. It is possible that thenumber of connections made to the unit under test could differ at thetroubleshooting station. For example, if a specific failure mode isknown from the testing station, a test operator you might only make afew connections to simulate that one specific test.

Once the repaired UUT has been disconnected, the subroutine 802 proceedsto 716 of subroutine 702, where the repaired UUT is shipped to the testset used for the first product testing. Subroutines 602 and 802 arerepeated until the UUT passes retest at 616, and is prepared forshipment at 620 as discussed above.

Adapting Equation (17) for subroutine 802, the average test time may beexpressed as: $\begin{matrix}{{\overset{\_}{T}}_{A} = {\frac{T_{C}}{n} + T_{L} + T_{T} + {\left( {{P_{C}T_{T}} + T_{D\quad 1} + T_{L}} \right) \times \left( \frac{1 - Y_{F}}{Y_{R}} \right)} + {T_{D\quad 1}.}}} & (20)\end{matrix}$

The average product test time is: $\begin{matrix}{{\overset{\_}{T}}_{B} = {\frac{T_{C}}{n} + T_{L} + T_{T} + {\left( {{P_{C}T_{T}} + T_{P\quad 2} + T_{D\quad 1} + T_{M\quad 1} + T_{R\quad 2} + T_{D\quad 2} + T_{M\quad 4} + T_{L}} \right) \times \left( \frac{1 - Y_{F}}{Y_{R}} \right)} + T_{D\quad 1} + {T_{S}.}}} & (21)\end{matrix}$

The average troubleshooting/repair and retest cost added to each productis:${{Cost}/{unit}} = {C_{\$\quad T} \times {\left( {{\overset{\_}{T}}_{B} - \left( {\frac{T_{C}}{n} + T_{L} + T_{T} + T_{D\quad 1} + T_{S}} \right)} \right).}}$The change in average test time caused by a change in the good test timeis given by:${\Delta\quad{\overset{\_}{T}}_{A}} = {{\Delta\quad{\overset{\_}{T}}_{B}} = {\left( {1 - {P_{C}\left( \frac{1 - Y_{F}}{Y_{R}} \right)}} \right) \times \Delta\quad{T_{T}.}}}$

The change in average test time caused by a change in the troubleshoottime is given by:${{\Delta\quad{\overset{\_}{T}}_{A}} = 0},{{\Delta\quad{\overset{\_}{T}}_{B}} = {\left( \frac{1 - Y_{F}}{Y_{R}} \right) \times \Delta\quad{T_{P\quad 2}.}}}$The change in average test time caused by a change in the repair time isgiven by:${{\Delta\quad{\overset{\_}{T}}_{A}} = 0},{{\Delta\quad{\overset{\_}{T}}_{B}} = {\left( \frac{1 - Y_{F}}{Y_{R}} \right) \times \Delta\quad{T_{R\quad 2}.}}}$

The change in average test time caused by a change in yield is given by:${{\Delta\quad{\overset{\_}{T}}_{A}} = {{- \frac{\left( {{P_{C}T_{T}} + T_{D\quad 1} + T_{L}} \right)}{Y_{R}}} \times \Delta\quad Y_{F}}};{{\Delta\quad{\overset{\_}{T}}_{B}} = {{- \frac{\left( {{P_{C}T_{T}} + T_{P\quad 2} + T_{D\quad 1} + T_{M\quad 1} + T_{R\quad 2} + T_{D\quad 2} + T_{M\quad 4} + T_{L}} \right)}{Y_{R}}} \times \Delta\quad Y_{F}}};$${{\Delta\quad{\overset{\_}{T}}_{A}} = {{- \left( {{P_{C}T_{T}} + T_{D\quad 1} + T_{L}} \right)}\left( {1 - Y_{F}} \right) \times \frac{Y_{R\quad 2} - Y_{R\quad 1}}{Y_{R\quad 2} \times Y_{R\quad 1}}}};{and}$${\Delta\quad{\overset{\_}{T}}_{B}} = {{- \left( {{P_{C}T_{T}} + T_{P\quad 2} + T_{D\quad 1} + T_{M\quad 1} + T_{R\quad 2} + T_{D\quad 2} + T_{M\quad 4} + T_{L}} \right)}\left( {1 - Y_{F}} \right) \times {\frac{Y_{R\quad 2} - Y_{R\quad 1}}{Y_{R\quad 2} \times Y_{R\quad 1}}.}}$

FIG. 9 is a flow diagram 900 of a fourth subroutine 902 according tomethod 200 of FIG. 2. Subroutine 902 provides for off-linetroubleshooting and off-line repairs. The flow diagram 900 includessteps 610-622 of subroutine 602, except at 622, a determination was madethat troubleshooting is performed off-line (i.e., not at the test setequipment used for the first test). Further, subroutine 902 proceeds toand includes 810-816 of subroutine 802, which represent off-linetroubleshooting.

Specifically, at 810, the failed UUT is disconnected in a time ofT_(D1), which as discussed above, depends on the complexity of theproduct and test equipment. At 812, the failed UUT is moved (i.e.,transported) to a troubleshooting facility. The moving time T_(M1)associated with transporting the failed UUT is product dependent. Asdiscussed above, the moving times T_(M1) through T_(M4) are denoted ashaving different times, for example, since the locations of the on-linetroubleshooting facilities, and on-line/off-line repair testsets/workstations may all be different.

At 814, the failed UUT undergoes troubleshooting, as discussed above,and once troubleshooting is complete, subroutine 802 proceeds to 816. At816, a determination is made whether repairs are to be performed at thetest system position (on-line). If the determination at 816affirmatively answered, the subroutine 902 proceeds to 818 of subroutine802, as discussed above.

If the determination is negatively answered, the subroutine 902 proceedsto 910, where the failed UUT is not repaired at the same test equipmentwhere the troubleshooting equipment is located. At 910, the troubleshotUUT is disconnected from the diagnostics equipment at a time of T_(D2).At 912, the troubleshot UUT is moved (e.g., shipped) for repair to anoff-line test system. The time associated with moving a UUT from anon-line test set to a workstation at an off-line test set is T_(M3). Asnoted above, the off-line test set may be at the same manufacturing andassembly facility 100 or located at another site, such as a vendor site.

The moving time differences between on-line and off-line troubleshootingand/or repair centers may illustratively be attributed to the length ofthe route taken from the test set or troubleshooting station, whichwould change the duration of the transit interval. As discussed herein,move time T_(M1) is the time required to move from the test system 104to the troubleshooting station 107. Move time T_(M2) is the timerequired to move from the test system 107 to a workstation at the repairstation 108. If the troubleshooting station 107 and the repair station108 are not close to each other, the times would be different. Move timeT_(M3) is the time required to move from the troubleshooting station 107to the repair station 108, which depending on the physical location ofthe various facilities, could be yet another interval. Lastly, move timeT_(M4) is the time required to move from a workstation at the repairstation 108 back to the test system 104, and should be a value veryclose to T_(M2). The move times T_(M) are kept separate to enhance thegenerality of the model. Once the troubleshot UUT has been shipped tothe off-line repair equipment, subroutine 902 proceeds to 714 whereappropriate repairs are made.

Once repairs of the UUT are complete, the subroutine 902 proceeds to 716of subroutine 702, where the repaired UUT is shipped to the test set forretest. Subroutines 602 and 902 are repeated until the UUT passes retestat 616, and is then prepared for shipment at 620 as discussed above.

Adapting Equation (17) for subroutine 902, the average test time may beexpressed as: $\begin{matrix}{{\overset{\_}{T}}_{A} = {\frac{T_{C}}{n} + T_{L} + T_{T} + {\left( {{P_{C}T_{T}} + T_{D\quad 1} + T_{L}} \right) \times \left( \frac{1 - Y_{F}}{Y_{R}} \right)} + {T_{D\quad 1}.}}} & (22)\end{matrix}$

The average product test time is: $\begin{matrix}{{\overset{\_}{T}}_{B} = {\frac{T_{C}}{n} + T_{L} + T_{T} + {\left( {{P_{C}T_{T}} + T_{P\quad 2} + T_{D\quad 1} + T_{M\quad 1} + T_{R\quad 3} + T_{M\quad 3} + T_{D\quad 2} + T_{M\quad 4} + T_{L}} \right) \times \left( \frac{1 - Y_{F}}{Y_{R}} \right)} + T_{D\quad 1} + {T_{S}.}}} & (23)\end{matrix}$

The average troubleshooting/repair and retest cost added to each productis:${{Cost}/{unit}} = {C_{\$\quad T} \times {\left( {{\overset{\_}{T}}_{B} - \left( {\frac{T_{C}}{n} + T_{L} + T_{T} + T_{D\quad 1} + T_{S}} \right)} \right).}}$The change in average test time caused by a change in the good test timeis given by:${\Delta\quad{\overset{\_}{T}}_{A}} = {{\Delta\quad{\overset{\_}{T}}_{B}} = {\left( {1 + {P_{C}\left( \frac{1 - Y_{F}}{Y_{R}} \right)}} \right) \times \Delta\quad{T_{T}.}}}$The change in average test time caused by a change in the troubleshoottime is given by:${{\Delta\quad{\overset{\_}{T}}_{A}} = 0},{{\Delta\quad{\overset{\_}{T}}_{B}} = {\left( \frac{1 - Y_{F}}{Y_{R}} \right) \times \Delta\quad{T_{P\quad 2}.}}}$The change in average test time caused by a change in the repair time isgiven by:${{\Delta\quad{\overset{\_}{T}}_{A}} = 0},{{\Delta\quad{\overset{\_}{T}}_{B}} = {\left( \frac{1 - Y_{F}}{Y_{R}} \right) \times \Delta\quad{T_{R\quad 3}.}}}$

The change in average test time caused by a change in yield is given by:${{\Delta\quad{\overset{\_}{T}}_{A}} = {{- \frac{\left( {{P_{C}T_{T}} + T_{D\quad 1} + T_{L}} \right)}{Y_{R}}} \times \Delta\quad Y_{F}}};$${{\Delta\quad{\overset{\_}{T}}_{B}} = {{- \frac{\left( {{P_{C}T_{T}} + T_{P\quad 2} + T_{D\quad 1} + T_{M\quad 1} + T_{R\quad 3} + T_{M\quad 3} + T_{D\quad 2} + T_{M\quad 4} + T_{L}} \right)}{Y_{R}}} \times \Delta\quad Y_{F}}};$${{\Delta\quad{\overset{\_}{T}}_{A}} = {{- \left( {{P_{C}T_{T}} + T_{D\quad 1} + T_{L}} \right)}\left( {1 - Y_{F}} \right) \times \frac{Y_{R\quad 2} - Y_{R\quad 1}}{Y_{R\quad 2} \times Y_{R\quad 1}}}};{and}$${\Delta\quad{\overset{\_}{T}}_{B}} = {{- \left( {T_{T} + T_{P\quad 2} + T_{D\quad 1} + T_{M\quad 1} + T_{R\quad 3} + T_{M\quad 3} + T_{D\quad 2} + T_{M\quad 4} + T_{L}} \right)}\left( {1 - Y_{F}} \right) \times {\frac{Y_{R\quad 2} - Y_{R\quad 1}}{Y_{R\quad 2} \times Y_{R\quad 1}}.}}$

Thus, the subroutines 602, 702, 802, and 902 form method 200 of FIG. 2.Referring to method 200 of FIG. 2, to generalize the process model it isassumed that the decision points are not fixed. Rather, it is assumedthat the decision is the proportion of times a particular path is taken.That is, depending on the circumstance of the failure, a test managermay choose to perform the troubleshooting on-line in some instances, andoff-line (at the troubleshooting station) at other times. If thefacility 100 is running high volume and high yields, a test managermight send all failures to a separate troubleshooting station so as notto slow down the throughput on a high speed line. Also, minor repairs,such as a loose connection or a cable that has been connected to thewrong location causes the failure, these minor repairs would most likelybe made at the test system, where testing could continue immediatelythereafter. If a major sub assembly needed to be replaced, a manager maydeem it better to send the failed sub assembly to an off-line repairposition. Because you have several options that may be exercisedindependently from one UUT to the next, the decision points are notbinary, but truly become proportions (i.e., what proportion of the timedo you troubleshoot at the test set, or what proportion of the time doyou repair at the test set. It is noted that the effect of havingdifferent yields at first test and retest is also included.

In one embodiment of the invention, a computer readable medium storesthe instructions

The resulting set of equations enable effective management of the testprocess and the resources consumed. The average time at the test systemis: $\begin{matrix}{{\overset{\_}{T}}_{A} = {\frac{T_{C}}{n} + T_{L} + T_{T} + T_{D\quad 1} + {\left( \frac{1 - Y_{F}}{Y_{R}} \right) \times \left\lbrack {{P_{C}T_{T}} + {L_{2}\left( {T_{P\quad 1} + {L_{3}T_{R\quad 1}} + {\left( {1 - L_{3}} \right)\left( {T_{D\quad 1} + T_{L}} \right)}} \right)} + {\left( {1 - L_{2}} \right)\left( {T_{D\quad 1} + T_{L}} \right)}} \right\rbrack} + {L_{2}L_{3}{T_{S}.}}}} & (24)\end{matrix}$The average product test time is: $\begin{matrix}{{\overset{\_}{T}}_{B} = {\frac{T_{C}}{n} + T_{L} + T_{T} + T_{D\quad 1} + T_{S} + {{\left( \frac{1 - Y_{F}}{Y_{R}} \right)\left\lbrack {{L_{2}\left( {{P_{C}T_{T}} + T_{P\quad 1} + {L_{3}\left( T_{R\quad 1} \right)} + {\left( {1 - L_{3}} \right)\left( {T_{D\quad 1} + T_{M\quad 2} + T_{R\quad 3} + T_{M\quad 4} + T_{L}} \right)}} \right)} + {\left( {1 - L_{2}} \right)\left( {{P_{C}T_{T}} + T_{P\quad 2} + T_{D\quad 1} + T_{M\quad 1} + T_{D\quad 2} + T_{M\quad 4} + T_{L} + {L_{4}\left( T_{R\quad 2} \right)} + {\left( {1 - D_{4}} \right)\left( {T_{R\quad 3} + T_{M\quad 3}} \right)}} \right)}} \right\rbrack}.}}} & (25)\end{matrix}$

Referring to FIG. 2, it is noted that L₁ represents a proportion(percentage) of units under test that passed testing at the online testset, and L₂ represents a proportion (percentage) of units under testthat are troubleshot at the online test set. Additionally, L₃ representsa proportion (percentage) of units under test that are repaired at theonline test set, while L₄ represents a proportion (percentage) of unitsunder test that are repaired at an off-line troubleshooting station.

Equation (24) provides the average amount of time a product will spendon the test system (i.e., the time the resource is tied up). Equation(24) is useful for performing capacity and utilization calculations.Equation (25) provides for the average amount of time a product spendsin the test process. Equation (25) is useful in assessing throughput andscheduling the operation. The fundamental difference between these twoequations is where the troubleshooting and repair operations areperformed. By experimenting with Equations (24) and (25), a tradeoff maybe observed between test system capacity consumed versus the throughputfor the product. The more that is offloaded from the test system toimprove capacity, the longer the average time it takes to get theproduct through the process.

To make an objective assessment among the alternatives, the average timeat each of the other workstations is provided below in Equations (26)through Equation (29). Since each product flows through the shippingoperation once, the average time at the shipping operation is:{overscore (T)}_(S)=T_(S). (26)

For the troubleshooting operation, the time at an independenttroubleshooting station is only considered. The time spenttroubleshooting at the test system is already included in the T_(A)calculation. The average time to repair is: $\begin{matrix}{{\overset{\_}{T}}_{TR} = {\left( {1 - L_{2}} \right)\left( \frac{1 - Y_{F}}{Y_{R}} \right){\left( {T_{P\quad 2} + T_{D\quad 2} + {L_{4}T_{R\quad 2}}} \right).}}} & (27)\end{matrix}$

The average time at the repair position is given by: $\begin{matrix}{{\overset{\_}{T}}_{R} = {\left( \frac{1 - Y_{F}}{Y_{R}} \right){{T_{R\quad 3}\left( {{L_{2}\left( {1 - L_{3}} \right)} + {\left( {1 - L_{2}} \right)\left( {1 - L_{4}} \right)}} \right)}.}}} & (28)\end{matrix}$

The average time at the move operation is given by: $\begin{matrix}{{{\overset{\_}{T}}_{M} = {\left( \frac{1 - Y_{F}}{Y_{R}} \right)\left( {{{L_{2}\left( {1 - L_{3}} \right)}\left( {T_{M\quad 2} + T_{M\quad 4}} \right)} + {\left( {1 - L_{2}} \right)\left( {T_{M\quad 1} + T_{M\quad 4} + {\left( {1 - L_{4}} \right)T_{M\quad 3}}} \right)}} \right)}},} & (29)\end{matrix}$where the “move operation” is a generalized reference to the compositeof T_(M1), T_(M2), T_(M3), & T_(M4). If you have specialized labor isrequired for performing this operation, Equation (29) will be used toestimate the amount of resources that are required.

The analysis of the change in average time consumed at the test systemyields the following: the change in average test time T_(A) caused by achange in the good test time is given by: $\begin{matrix}{{\Delta\quad{\overset{\_}{T}}_{A}} = {\left( {1 + {P_{C}\left( \frac{1 - Y_{F}}{Y_{R}} \right)}} \right) \times \Delta\quad{T_{T}.}}} & (30)\end{matrix}$

The change in average test time T_(A) caused by a change in thetroubleshoot time is given by: $\begin{matrix}{{\Delta\quad{\overset{\_}{T}}_{A}} = {\left( \frac{1 - Y_{F}}{Y_{R}} \right)L_{2} \times \Delta\quad{T_{P\quad 1}.}}} & (31)\end{matrix}$

The change in average test time T_(A) caused by a change in the repairtime is given by: $\begin{matrix}{{\Delta\quad{\overset{\_}{T}}_{A}} = {\left( \frac{1 - Y_{F}}{Y_{R}} \right)L_{2}L_{3} \times \Delta\quad{T_{R\quad 1}.}}} & (32)\end{matrix}$

The change in average test time T_(A) caused by a change in first testyield is given by: Δ{overscore(T)}_(A)=−(P_(C)T_(T)+L₂(T_(P1)+L₃T_(R1)+(1−L₃)(T_(D1)+T_(L)))+(1−L₂)(T_(D1)+T_(L)))×ΔY_(F).(33)

The change in average test time T_(A) caused by a change in retest yieldis given by: $\begin{matrix}{{\Delta\quad{\overset{\_}{T}}_{A}} = {{- \begin{pmatrix}\left( {{P_{C}T_{T}} + {L_{2}\left( {T_{P\quad 1} + {L_{3}T_{R\quad 1}} + {\left( {1 - L_{3}} \right)\left( {T_{D\quad 1} + T_{L}} \right)}} \right)} +} \right. \\{\left( {1 - L_{2}} \right)\left( {T_{D\quad 1} + T_{L}} \right)}\end{pmatrix}}\left( {1 - Y_{F}} \right){\left( \frac{Y_{R\quad 2} - Y_{R\quad 1}}{Y_{R\quad 2}Y_{R\quad 1}} \right).}}} & (34)\end{matrix}$

Changes in these parameters affect the average product test time asfollows. The change in average product test time T_(B) caused by achange in the good test time is given by: $\begin{matrix}{{{\Delta\quad{\overset{\_}{T}}_{B}} = {\left( {1 + {P_{C}\left( \frac{1 - Y_{F}}{Y_{R}} \right)}} \right) \times \Delta\quad T_{T}}},} & (35)\end{matrix}$

where T_(B) id the average time that a product spends in the entire testprocess. This is the throughput affecting time for the product.

The change in average product test time T_(B) caused by a change in thetroubleshoot time is given by: $\begin{matrix}{{{\Delta\quad{\overset{\_}{T}}_{B}} = {\left( \frac{1 - Y_{F}}{Y_{R}} \right)L_{2} \times \Delta\quad T_{P\quad 1}}};} & (36) \\{{\Delta\quad{\overset{\_}{T}}_{B}} = {\left( \frac{1 - Y_{F}}{Y_{R}} \right)\left( {1 - L_{2}} \right) \times \Delta\quad T_{P\quad 2}}} & (37)\end{matrix}$

The change in average product test time T_(B) caused by a change in therepair time is given by: $\begin{matrix}{{\Delta\quad{\overset{\_}{T}}_{B}} = {\left( \frac{1 - Y_{F}}{Y_{R}} \right)L_{2}L_{3} \times \Delta\quad T_{R\quad 1}}} & (38) \\{{\Delta\quad{\overset{\_}{T}}_{B}} = {\left( \frac{1 - Y_{F}}{Y_{R}} \right)\left( {1 - L_{2}} \right)L_{4} \times \Delta\quad T_{R\quad 2}}} & (39) \\{{\Delta\quad{\overset{\_}{T}}_{B}} = {\left( \frac{1 - Y_{F}}{Y_{R}} \right)\left( {{L_{2}\left( {1 - L_{3}} \right)} + {\left( {1 - L_{2}} \right)\left( {1 - L_{4}} \right)}} \right) \times \Delta\quad T_{R\quad 3}}} & (40)\end{matrix}$

The change in average product test time T_(B) caused by a change infirst test yield is given by: $\begin{matrix}{{\Delta\quad{\overset{\_}{T}}_{B}} = {{- \begin{bmatrix}{L_{2}\left( {{P_{C}T_{T}} + T_{P\quad 1} + {L_{3}T_{R\quad 1}} +} \right.} \\{\left. {\left( {1 - L_{3}} \right)\left( {T_{D\quad 1} + T_{M\quad 2} + T_{R\quad 3} + T_{M\quad 4} + T_{L}} \right)} \right) +} \\{\left( {1 - L_{2}} \right)\begin{pmatrix}{{P_{C}T_{T}} + T_{P\quad 2} + T_{D\quad 1} + T_{M\quad 1} +} \\{T_{D\quad 2} + T_{M\quad 4} + T_{L} + {L_{4}T_{R\quad 2}} +} \\{\left( {1 - L_{4}} \right)\left( {T_{R\quad 3} + T_{M\quad 3}} \right)}\end{pmatrix}}\end{bmatrix}}{\Delta Y}_{F}}} & (41)\end{matrix}$

The change in average product test time T_(B) caused by a change inretest yield is given by: $\begin{matrix}{{\Delta\quad{\overset{\_}{T}}_{B}} = {{- \begin{bmatrix}{{L_{2}\begin{pmatrix}{{P_{C}T_{T}} + T_{P\quad 1} + {L_{3}T_{R\quad 1}} + \left\lbrack \left( {1 - L_{3}} \right) \right.} \\\left. \left( {T_{D\quad 1} + T_{M\quad 4} + T_{R\quad 3} + T_{M\quad 4} + T_{L}} \right) \right\rbrack\end{pmatrix}} +} \\{\left( {1 - L_{2}} \right)\begin{pmatrix}{{P_{C}T_{T}} + T_{P\quad 2} + T_{D\quad 1} + T_{M\quad 1} + T_{D\quad 2} + T_{M\quad 4} +} \\{T_{L} + {L_{4}T_{R\quad 2}} + {\left( {1 - L_{4}} \right)\left( {T_{R\quad 3} + T_{M\quad 3}} \right)}}\end{pmatrix}}\end{bmatrix}}\left( {1 - Y_{F}} \right)\left( \frac{Y_{R\quad 2} - Y_{R\quad 1}}{Y_{R\quad 2}Y_{R\quad 1}} \right)}} & (42)\end{matrix}$

The present invention overcomes the deficiencies of the prior art byaccounting for the possible (and most probable) differences between testyield occurring during initial (first) testing and test yields aftertroubleshooting and repair have occurred. Accordingly, the presentinvention provides a more accurate method of planning the amount of time(i.e., the average test time) it takes during test operations.

The present invention may be implemented by one or more controllers 120that are in communication with the test operations 102. Although notshown in FIG. 1, historical databases may be utilized to collect trenddata to provide actual times associated with preparing a test stationfor test (T_(C)), loading a unit under test (T_(L)), performing theactual diagnostics (T_(P)), performing the actual repairs (T_(R)),disconnecting the UUT after troubleshooting and/or repairs are complete(T_(D)), and shipping operations (T_(S)).

Further distinctions may be made as between performing on-linetroubleshooting at the current test equipment, and off-linetroubleshooting at the other diagnostic/test equipment. It has beenshown that the times associated between on-line and off-linetroubleshooting may vary significantly, depending on the type, location,and capabilities of the off-line equipment, as compared to the on-linetest set equipment.

A similar analysis is also applicable to the repair test set. That is,the times associated between on-line and off-line repairs may varysignificantly, depending on the type, location, and capabilities of theoff-line test set equipment, as compared to the on-line test setequipment.

The at least one controller of the present invention is able toaccurately predict the average test time to perform the test operationsfor finished product created by a manufacturing and assembly facility100. The basic models defined by Equations (4), (5), and (6), and moresophisticated models of Equations (41) and (42) enable test operationplanners to more accurately determine their equipment requirements,staffing needs, and how to better allocate resources (e.g., capitalresources) to improve product throughput during test operations, thanthe current models and estimates used today.

Although various embodiments that incorporate the teachings of thepresent invention have been shown and described in detail herein, thoseskilled in the art can readily devise many other varied embodiments thatstill incorporate these teachings.

1. A method of establishing an average test time (T_(A)), comprising:determining a first time interval (T_(G)) nominally associated withnon-failing testing of a unit under test (UUT); determining a secondtime interval (T_(PR)) nominally associated with troubleshooting andrepairing a failed unit under test; determining a percent yield (Y)nominally associated with a proportion of non-failing units under test,wherein said average test time (T_(A)) is defined asT_(A)=T_(G)+(T_(G)+T_(PR))((1−Y)/Y)).
 2. The method of claim 1, whereinsaid determining said percent yield (Y) further comprises: determining afirst yield (Y_(F)) associated with units of said product passing whereno failures occurring during said testing; and determining a secondyield (Y_(R)) associated with units of said product passing retest afterfailing initial testing.
 3. The method of claim 2, wherein said totalaverage test time is T_(A)=T_(G)+(T_(G)+T_(PR))((1−Y_(F))/Y_(R))). 4.The method of claim 3, further comprising: determining a percent of testthat is completed (P_(C)) prior to termination from a test failure, saidaverage test time beingT_(A)=T_(G)+(P_(C)T_(G)+T_(PR))((1−Y_(F))/Y_(R)).
 5. The method of claim4, further comprising: determining a number of test systems required toperform said testing, said number of test systems required beingQT_(A)/T_(SA), wherein Q represent a number of units being tested andT_(SA) represents a time a test asset is available within an allottedtime period.
 6. The method of claim 4, further comprising: determiningstaffing levels required to perform said testing, wherein said staffinglevels required is QT_(A)/T_(AA), wherein Q represent a number of unitsbeing tested and T_(AA) represents a time each staff member is availablewithin an allotted time period.
 7. The method of claim 4, furthercomprising: determining average cost per unit, where said average costper unit is a product of cost per unit (C_($T)) and said total averagetest time (T_(A)).
 8. The method of claim 7, further comprising:determining average cost per unit for troubleshooting, repair, andretest, where said average cost per unit for troubleshooting, repair,and retest is (C_($T)) (T_(A)-T_(G)).
 9. The method of claim 4, furthercomprising: determining a change in average test time caused by a changein said first time interval associated with testing a unit under testwhere no failures occur during said testing, where said change inaverage test time is${\Delta\quad\overset{\_}{T}} = {\left( {1 + {P_{C}\left( \frac{1 - Y_{F}}{Y_{R}} \right)}} \right) \times \Delta\quad{T_{G}.}}$10. The method of claim 4, further comprising: determining a change inaverage test time caused by a change in said second time intervalassociated with testing a repaired unit under test during said testing,where said change in average test time is${\Delta\quad\overset{\_}{T}} = {\left( \frac{1 - Y_{F}}{Y_{R}} \right) \times \Delta\quad{T_{PR}.}}$11. The method of claim 4, further comprising: determining a change inaverage test time caused by a change in said first yield (Y_(F)), wheresaid change in average test time is${\Delta\quad\overset{\_}{T}} = {{- \frac{\left( {{P_{C}T_{G}} + T_{PR}} \right)}{Y_{R}}} \times \Delta\quad{Y_{F}.}}$12. The method of claim 4, further comprising: determining a change inaverage test time caused by a change in said second yield (Y_(R)), wheresaid change in average test time is${\Delta\quad\overset{\_}{T}} = {{- \left( {{P_{C}T_{G}} + T_{PR}} \right)}\left( {1 - Y_{F}} \right) \times {\frac{Y_{R\quad 2} - Y_{R\quad 1}}{Y_{R\quad 2} \times Y_{R\quad 1}}.}}$13. The method of claim 4, further comprising: determining percent ofutilization of said test, where said percent of${Utilization} = {\frac{Q \times \overset{\_}{T}}{N_{S} \times T_{SA}} \times 100{\%.}}$14. The method of claim 4, wherein determining said first time intervalT_(G) comprises: determining a load time component T_(L) associated withloading a unit under test to a test set; determining a test timecomponent T_(T) associated with testing said unit under test; anddetermining a time interval T_(C) to prepare a test system forperforming product testing.
 15. The method of claim 14, whereindetermining said second time interval T_(PR) comprises: determining atroubleshooting time component T_(P) associated with troubleshooting adefective unit under test; determining a repair time component T_(R)associated with repairing said defective unit under test for aparticular test set; and determining a disconnect time component T_(D)associated with disconnecting said unit under test from said test set.16. The method of claim 15, wherein: said determining a troubleshootingtime component comprises determining a time interval T_(P1) associatedwith performing on-line troubleshooting at a test set where testing ofsaid UUT was performed; said determining a repair time componentcomprises determining a time interval T_(R1) associated with performingon-line repairs at said test set where testing of said UUT wasperformed; and said determining a disconnect time component comprisesdetermining a time interval T_(D1) associated with disconnecting saidunit under test from said on-line test set.
 17. The method of claim 16,wherein said average test time T_(A) is:${\overset{\_}{T_{A}} = {\left( \frac{T_{C}}{n} \right) + T_{L} + T_{T} + {\left( {{P_{C}T_{T}} + T_{P\quad 1} + T_{R\quad 1}} \right) \times \left( \frac{1 - Y_{F}}{Y_{R}} \right)} + T_{D\quad 1} + T_{S}}},$where n represents an average lot size of said product, and T_(S) is atime interval to transport said unit under test after testing isperformed.
 18. The method of claim 15, wherein: said determining atroubleshooting time component comprises determining a time intervalT_(P1) associated with performing on-line troubleshooting at a test setwhere testing of said UUT was performed; said determining a repair timecomponent comprises determining a time interval T_(R3) associated withperforming off-line repairs at a workstation that is different fromwhere troubleshooting of said UUT was performed; and said determining adisconnect time component comprises determining a time interval T_(D1)associated with disconnecting said unit under test from said on-linetest set where said testing of said UUT was performed.
 19. The method ofclaim 18, wherein said average test time T_(A) is:${\overset{\_}{T_{A}} = {\left( \frac{T_{C}}{n} \right) + T_{L} + T_{T} + {\left( {{P_{C}T_{T}} + T_{P\quad 1} + T_{D\quad 1} + T_{L}} \right) \times \left( \frac{1 - Y_{F}}{Y_{R}} \right)} + T_{D\quad 1}}},$where n represents an average lot size of said product.
 20. The methodof claim 18, further comprising: determining a move time interval (M₂)associated with transferring a failed UUT from said test set associatedwith performing online troubleshooting of said UUT, to an off-linerepair facility; and determining a move time interval (M₄) associatedwith time to transfer a repaired UUT from said workstation associatedwith off-line repair to said test set associated with performing onlinetesting of said UUT.
 21. The method of claim 20, further comprising:determining an average product test time TB, said average product testtime being defined as:${{\overset{\_}{T}}_{B} = {\frac{T_{C}}{n} + T_{L} + T_{T} + {\left( {{P_{C}T_{T}} + T_{P\quad 1} + T_{D\quad 1} + T_{M\quad 2} + T_{R\quad 3} + T_{M\quad 4} + T_{L}} \right) \times \left( \frac{1 - Y_{F}}{Y_{R}} \right)} + T_{D\quad 1} + T_{S\quad}}},$where n represents an average lot size of said product, and T_(S) is atime interval to transport said unit under test after testing isperformed.
 22. The method of claim 15, wherein: said determining atroubleshooting time component comprises determining a time intervalT_(P2) associated with performing troubleshooting at a test set that isoff-line from where testing of said UUT was performed; said determininga repair time component comprises determining a time interval T_(R2)associated with performing on-line repairs at said off-line test set;said determining a disconnect time component comprises determining afirst time interval T_(D1) associated with disconnecting said unit undertest from said on-line test set where said testing of said UUT wasperformed; and said determining a disconnect time component comprisesdetermining a second time interval T_(D2) associated with disconnectingsaid unit under test from said test set where said off-linetroubleshooting of said UUT was performed.
 23. The method of claim 22,wherein said average test time T_(A) is:${\overset{\_}{T_{A}} = {\left( \frac{T_{C}}{n} \right) + T_{L} + T_{T} + {\left( {{P_{C}T_{T}} + T_{D\quad 1} + T_{L}} \right) \times \left( \frac{1 - Y_{F}}{Y_{R}} \right)} + T_{D\quad 1}}},$where n represents an average lot size of said product.
 24. The methodof claim 22, further comprising: determining a move time interval (M₁)associated with transferring a failed UUT from said test set associatedwith performing on-line testing of said UUT, to a test set associatedwith performing off-line troubleshooting of said UUT; and determining amove time interval (M4) associated with transferring a repaired UUT froma test set associated with performing off-line troubleshooting withon-line repair of said UUT, to said test set associated with performingonline testing of said UUT.
 25. The method of claim 24, furthercomprising: determining an average product test time TB, said averageproduct test time being defined as:${{\overset{\_}{T}}_{B} = {\frac{T_{C}}{n} + T_{L} + T_{T} + {\left( {{P_{C}T_{T}} + T_{P\quad 2} + T_{D\quad 1} + T_{M\quad 1} + T_{R\quad 2} + T_{D\quad 2} + T_{M\quad 4} + T_{L}} \right) \times \left( \frac{1 - Y_{F}}{Y_{R}} \right)} + T_{D\quad 1} + T_{S}}},$where n represents an average lot size of said product, and T_(S) is atime interval to transport said unit under test after testing isperformed.
 26. The method of claim 15, wherein: said determining atroubleshooting time component comprises determining a time intervalT_(P2) associated with performing troubleshooting at a test set that isoff-line from where testing of said UUT was performed; said determininga repair time component comprises determining a time interval T_(R3)associated with performing off-line repairs at a test set that isdifferent from where troubleshooting of said UUT was performed; saiddetermining a disconnect time component comprises determining a timeinterval T_(D1) associated with disconnecting said unit under test fromsaid on-line test set where said testing of said UUT was performed; andsaid determining a disconnect time component comprises determining asecond time interval T_(D2) associated with disconnecting said unitunder test from said test set where said off-line troubleshooting ofsaid UUT was performed.
 27. The method of claim 26, wherein said averagetest time T_(A) is:${\overset{\_}{T_{A}} = {\left( \frac{T_{C}}{n} \right) + T_{L} + T_{T} + {\left( {{P_{C}T_{T}} + T_{D\quad 1} + T_{L}} \right) \times \left( \frac{1 - Y_{F}}{Y_{R}} \right)} + T_{D\quad 1}}},$where n represents an average lot size of said product.
 28. The methodof claim 26, further comprising: determining a move time interval (MI)associated with transferring a failed UUT from said test set associatedwith performing on-line testing of said UUT, to a test set associatedwith performing off-line troubleshooting of said UUT; determining a movetime interval (M₃) associated with transferring a troubleshot UUT fromsaid test set associated with performing off-line troubleshooting ofsaid UUT, to a workstation associated with performing off-line repair ofsaid UUT; and determining a move time interval (M₄) associated withtransferring a repaired UUT from a workstation associated withperforming off-line repair of said UUT, to said test set associated withperforming online testing of said UUT.
 29. The method of claim 28,further comprising: determining an average product test time TB, saidaverage product test time being defined as:${\overset{\_}{T}}_{B} = {\frac{T_{C}}{n} + T_{L} + T_{T} + {\left( {{P_{C}T_{T}} + T_{P\quad 2} + T_{D\quad 1} + T_{M\quad 1} + T_{R\quad 3} + T_{M\quad 3} + T_{D\quad 2} + T_{M\quad 4} + T_{L}} \right) \times \left( \frac{1 - Y_{F}}{Y_{R}} \right)} + T_{D\quad 1} + T_{S}}$, where n represents an average lot size of said product, and T_(S) is atime interval to transport said unit under test after testing isperformed.
 30. The method of claim 15, wherein said average test timeis:${{\overset{\_}{T}}_{A} = {\frac{T_{C}}{n} + T_{L} + T_{T} + T_{D\quad 1} + {\left( \frac{1 - Y_{F}}{Y_{R}} \right) \times \left\lbrack {{P_{C}T_{T}} + {L_{2}\left( {T_{P\quad 1} + {L_{3}T_{R\quad 1}} + {\left( {1 - L_{3}} \right)\left( {T_{D\quad 1} + T_{L}} \right)}} \right)} + {\left( {1 - L_{2}} \right)\left( {T_{D\quad 1} + T_{L}} \right)}} \right\rbrack} + {L_{2}L_{3}T_{S}}}},$and wherein: L₂ represents a percentage of units under test that aretroubleshot at the online test set; L₃ represents a percentage of unitsunder test that are repaired at the online test set; T_(D1) represents atime interval associated with disconnecting said unit under test fromsaid on-line test set where said testing of said UUT was performed;T_(P1) represents a time interval associated with performing on-linetroubleshooting at a test set where testing of said UUT was performed;T_(R1) represents a time interval associated with performing on-linerepairs at said test set where testing of said UUT was performed; andT_(S) represents a time interval to transport said unit under test aftertesting is performed.
 31. The method of claim 15, wherein said averageproduct test time is:${{\overset{\_}{T}}_{B} = {\frac{T_{C}}{n} + T_{L} + T_{T} + T_{D\quad 1} + T_{S} + {\left( \frac{1 - Y_{F}}{Y_{R}} \right)\left\lbrack \quad{{L_{2}\left( {{P_{C}T_{T}} + T_{P\quad 1} + {L_{3}\left( T_{R\quad 1} \right)} + {\left( {1 - L_{3}} \right)\left( {T_{D\quad 1} + T_{M\quad 2} + T_{R\quad 3} + T_{M\quad 4} + T_{L}} \right)}} \right)} + {\left( {1 - L_{2}} \right)\left( {{P_{C}T_{T}} + T_{P\quad 2} + T_{D\quad 1} + T_{M\quad 1} + T_{D\quad 2} + T_{M\quad 4} + T_{L} + {L_{4}\left( T_{R\quad 2} \right)} + {\left( {1 - L_{4}} \right)\left( {T_{R\quad 3} + T_{M\quad 3}} \right)}} \right)}} \right\rbrack}}},$and wherein: L₂ represents a percentage of units under test that aretroubleshot at the online test set; L₃ represents a percentage of unitsunder test that are repaired at the online test set; L₄ represents apercentage of units under test that are repaired at an off-linetroubleshooting station; T_(D1) represents a time interval associatedwith disconnecting said unit under test from said on-line test set wheresaid testing of said UUT was performed; T_(D2) represents a second timeinterval associated with disconnecting said unit under test from saidtest set where said off-line troubleshooting of said UUT was performed;T_(P1) represents a time interval associated with performing on-linetroubleshooting at a test set where testing of said UUT was performed;T_(P2) represents a time interval associated with performingtroubleshooting at a test set that is off-line from where testing ofsaid UUT was performed; T_(R1) represents a time interval associatedwith performing on-line repairs at said test set where testing of saidUUT was performed; T_(S) represents a time interval to transport saidunit under test after testing is performed; T_(R2) represents a timeinterval associated with performing on-line repairs at said off-linetest set used for troubleshooting; T_(R3) represents a time intervalT_(R3) associated with performing off-line repairs at a workstation thatis different from where troubleshooting of said UUT was performed;T_(M1) represents a move time interval associated with transferring afailed UUT from said test set associated with performing on-line testingof said UUT, to a test set associated with performing off-linetroubleshooting of said UUT; T_(M2) represents a move time intervalassociated with transferring a failed UUT from said test set associatedwith performing online troubleshooting of said UUT, to a workstation atan off-line repair facility; T_(M3) represents a move time intervalassociated with transferring a troubleshot UUT from said test setassociated with performing off-line troubleshooting of said UUT, to aworkstation associated with performing off-line repair of said UUT;T_(M4) represents a move time interval associated with transferring arepaired UUT from a workstation associated with performing off-linerepair of said UUT, to said test set associated with performing onlinetesting of said UUT; and n represents an average lot size of saidproduct.
 32. Apparatus for establishing an average test time (T_(A)),comprising: means for determining a first time interval (T_(G))nominally associated with non-failing testing of a unit under test(UUT); means for determining a second time interval (T_(PR)) nominallyassociated with troubleshooting and repairing a failed unit under test;means for determining a percent yield (Y) nominally associated with aproportion of non-failing units under test, wherein said average testtime (T_(A)) is defined as T_(A)=T_(G)+(T_(G)+T_(PR))((1−Y)/Y)).
 33. Theapparatus of claim 32, wherein said means for determining said percentyield (Y) further comprises: means for determining a first yield (Y_(F))associated with units of said product passing where no failuresoccurring during said testing; and means for determining a second yield(Y_(R)) associated with units of said product passing retest afterfailing initial testing.
 34. The apparatus of claim 33, wherein saidtotal average test time is T_(A)=T_(G)+(T_(G)+T_(PR))((1−Y_(F))/Y_(R))).35. The apparatus of claim 34, further comprising: means for determininga percent of test that is completed (P_(C)) prior to termination from atest failure, said average test time beingT_(A)=T_(G)+(P_(C)T_(G)+T_(PR))((1−Y_(F))/Y_(R)).
 36. The apparatus ofclaim 35, wherein said determining said first time interval T_(G)comprises: means for determining a load time component T_(L) associatedwith loading a unit under test to a test set; means for determining atest time component T_(T) associated with testing said unit under test;and means for determining a time interval T_(C) to prepare a test systemfor performing product testing.
 37. The apparatus of claim 36, whereinsaid determining said second time interval T_(PR) comprises: means fordetermining a troubleshooting time component T_(P) associated withtroubleshooting a defective unit under test; means for determining arepair time component T_(R) associated with repairing said defectiveunit under test for a particular test set; and means for determining adisconnect time component T_(D) associated with disconnecting said unitunder test from said test set.
 38. The apparatus of claim 37, wherein:said means for determining a troubleshooting time component comprisesdetermining a time interval T_(P1) associated with performing on-linetroubleshooting at a test set where testing of said UUT was performed;said means for determining a repair time component comprises determininga time interval T_(R1) associated with performing on-line repairs atsaid test set where testing of said UUT was performed; and said meansfor determining a disconnect time component comprises determining a timeinterval T_(D1) associated with disconnecting said unit under test fromsaid on-line test set.
 39. The apparatus of claim 38, wherein saidaverage test time T_(A) is:${\overset{\_}{T_{A}} = {\left( \frac{T_{C}}{n} \right) + T_{L} + T_{T} + {\left( {{P_{C}T_{T}} + T_{P\quad 1} + T_{R\quad 1}} \right) \times \left( \frac{1 - Y_{F}}{Y_{R}} \right)} + T_{D\quad 1} + T_{S}}},$where n represents an average lot size of said product, and T_(S) is atime interval to ship said unit under test after repairs are performed.40. A computer readable medium including software instructions whichwhen executed by a processor perform a method for establishing anaverage test time (T_(A)), comprising: comprising: determining a firsttime interval (T_(G)) nominally associated with non-failing testing of aunit under test (UUT); determining a second time interval (T_(PR))nominally associated with troubleshooting and repairing a failed unitunder test; determining a percent yield (Y) nominally associated with aproportion of non-failing units under test, wherein said average testtime (T_(A)) is defined as T_(A)=T_(G)+(T_(G)+T_(PR))((1−Y)/Y)).
 41. Thecomputer readable medium of claim 40, wherein said determining saidpercent yield (Y) further comprises: determining a first yield (Y_(F))associated with units of said product passing where no failuresoccurring during said testing; and determining a second yield (Y_(R))associated with units of said product passing retest after failinginitial testing.
 42. The computer readable medium of claim 41, whereinsaid total average test time isT_(A)=T_(G)+(T_(G)+T_(PR))((1−Y_(F))/Y_(R))).
 43. The computer readablemedium of claim 42, further comprising: determining a percent of testthat is completed (P_(C)) prior to termination from a test failure, saidaverage test time beingT_(A)=T_(G)+(P_(C)T_(G)+T_(PR))((1−Y_(F))/Y_(R)).
 44. The computerreadable medium of claim 43, wherein said determining said first timeinterval T_(G) comprises: determining a load time component T_(L)associated with loading a unit under test to a test set; determining atest time component T_(T) associated with testing said unit under test;and determining a time interval T_(C) to prepare a test system forperforming product testing.
 45. The computer readable medium of claim44, wherein said determining said second time interval T_(PR) comprises:determining a troubleshooting time component T_(P) associated withtroubleshooting a defective unit under test; determining a repair timecomponent T_(R) associated with repairing said defective unit under testfor a particular test set; and determining a disconnect time componentT_(D) associated with disconnecting said unit under test from said testset.
 46. The computer readable medium of claim 45, wherein: saiddetermining a troubleshooting time component comprises determining atime interval T_(P1) associated with performing on-line troubleshootingat a test set where testing of said UUT was performed; said determininga repair time component comprises determining a time interval T_(R1)associated with performing on-line repairs at said test set wheretesting of said UUT was performed; and said determining a disconnecttime component comprises determining a time interval T_(D1) associatedwith disconnecting said unit under test from said on-line test set. 47.The computer readable medium of claim 46, wherein said average test timeT_(A) is:${\overset{\_}{T_{A}} = {\left( \frac{T_{C}}{n} \right) + T_{L} + T_{T} + {\left( {{P_{C}T_{T}} + T_{P\quad 1} + T_{R\quad 1}} \right) \times \left( \frac{1 - Y_{F}}{Y_{R}} \right)} + T_{D\quad 1} + T_{S}}},$where n represents an average lot size of said product, and T_(S) is atime interval to ship said unit under test after repairs are performed.